House Price Prediction with Bayesian Model Averaging

Bivariate Analysis

Continuous Variables

Target Correlation Analysis

Target Predictor Correlation CI.Lower CI.Upper p.value
price.log Overall.Qual 0.8206 0.7971 0.8416 0.000
price.log area.log 0.7466 0.7150 0.7752 0.000
price.log Garage.Cars 0.6826 0.6446 0.7172 0.000
price.log Kitchen.Qual 0.6668 0.6273 0.7028 0.000
price.log Exter.Qual 0.6646 0.6249 0.7008 0.000
price.log age.log -0.6511 -0.6886 -0.6102 0.000
price.log X1st.Flr.SF.log 0.6489 0.6077 0.6865 0.000
price.log age.garage.log -0.6253 -0.6650 -0.5822 0.000
price.log Bsmt.Qual 0.6213 0.5778 0.6613 0.000
price.log Full.Bath 0.5905 0.5444 0.6330 0.000
price.log age.remod.log -0.5819 -0.6251 -0.5352 0.000
price.log Fireplace.Qu 0.5688 0.5211 0.6130 0.000
price.log TotRms.AbvGrd.log 0.5474 0.4981 0.5933 0.000
price.log Fireplaces 0.5318 0.4813 0.5788 0.000
price.log Heating.QC 0.4922 0.4389 0.5419 0.000
price.log Open.Porch.SF.log 0.4706 0.4160 0.5218 0.000
price.log Garage.Area.log 0.4522 0.3965 0.5046 0.000
price.log Mas.Vnr.Area.log 0.4224 0.3650 0.4766 0.000
price.log Wood.Deck.SF.log 0.4179 0.3602 0.4724 0.000
price.log BsmtFin.Type.1 0.4177 0.3600 0.4722 0.000
price.log Lot.Area.log 0.3956 0.3368 0.4514 0.000
price.log Total.Bsmt.SF.log 0.3952 0.3364 0.4510 0.000
price.log Bsmt.Exposure 0.3767 0.3169 0.4335 0.000
price.log Bsmt.Full.Bath 0.3262 0.2641 0.3855 0.000
price.log Half.Bath 0.3223 0.2601 0.3819 0.000
price.log Lot.Shape -0.2985 -0.3591 -0.2353 0.000
price.log Garage.Finish 0.2858 0.2222 0.3470 0.000
price.log Bedroom.AbvGr 0.2721 0.2080 0.3338 0.000
price.log Lot.Area 0.2527 0.1881 0.3152 0.000
price.log Enclosed.Porch.log -0.2408 -0.3037 -0.1757 0.000
price.log Bsmt.Unf.SF.sqrt 0.1960 0.1299 0.2605 0.000
price.log X2nd.Flr.SF.log 0.1768 0.1102 0.2418 0.000
price.log Screen.Porch.log 0.0956 0.0279 0.1624 0.006
price.log Low.Qual.Fin.SF.log -0.0901 -0.1571 -0.0224 0.009
price.log Overall.Cond -0.0757 -0.1429 -0.0079 0.029
price.log Mo.Sold 0.0593 -0.0087 0.1266 0.087
price.log BsmtFin.SF.2.log -0.0142 -0.0820 0.0538 0.683
price.log Yr.Sold 0.0119 -0.0561 0.0797 0.732
price.log X3Ssn.Porch 0.0043 -0.0636 0.0721 0.902
price.log X3Ssn.Porch.log -0.0002 -0.0681 0.0677 0.996

Predictor Regression Summary

term r.squared adj.r.squared sigma statistic p.value df logLik AIC BIC deviance df.residual
Overall.Qual 0.673 0.673 0.218 1715.562 0.000 2 86.578 -167.155 -152.977 39.676 832
area.log 0.557 0.557 0.254 1047.935 0.000 2 -40.148 86.297 100.476 53.766 832
Garage.Cars 0.466 0.465 0.279 725.801 0.000 2 -118.529 243.057 257.236 64.884 832
Kitchen.Qual 0.445 0.444 0.285 665.940 0.000 2 -134.869 275.737 289.916 67.477 832
Exter.Qual 0.442 0.441 0.286 658.145 0.000 2 -137.044 280.088 294.267 67.830 832
age.log 0.424 0.423 0.290 612.343 0.000 2 -150.063 306.125 320.304 69.981 832
X1st.Flr.SF.log 0.421 0.420 0.291 605.003 0.000 2 -152.187 310.374 324.552 70.338 832
age.garage.log 0.391 0.390 0.298 534.305 0.000 2 -173.225 352.449 366.628 73.978 832
Bsmt.Qual 0.386 0.385 0.299 523.005 0.000 2 -176.688 359.375 373.554 74.595 832
Full.Bath 0.349 0.348 0.308 445.377 0.000 2 -201.289 408.578 422.757 79.128 832
age.remod.log 0.339 0.338 0.311 426.025 0.000 2 -207.655 421.310 435.489 80.345 832
Fireplace.Qu 0.324 0.323 0.314 397.989 0.000 2 -217.053 440.106 454.285 82.176 832
TotRms.AbvGrd.log 0.300 0.299 0.320 356.030 0.000 2 -231.527 469.054 483.232 85.079 832
Fireplaces 0.283 0.282 0.324 328.169 0.000 2 -241.422 488.845 503.023 87.122 832
Heating.QC 0.242 0.241 0.333 265.946 0.000 2 -264.409 534.819 548.997 92.059 832
Open.Porch.SF.log 0.221 0.221 0.337 236.700 0.000 2 -275.668 557.335 571.514 94.578 832
Garage.Area.log 0.205 0.204 0.341 213.916 0.000 2 -284.654 575.308 589.487 96.639 832
Mas.Vnr.Area.log 0.178 0.177 0.346 180.681 0.000 2 -298.120 602.239 616.418 99.810 832
Wood.Deck.SF.log 0.175 0.174 0.347 176.059 0.000 2 -300.027 606.055 620.233 100.268 832
BsmtFin.Type.1 0.174 0.173 0.347 175.840 0.000 2 -300.118 606.235 620.414 100.290 832
Lot.Area.log 0.157 0.156 0.351 154.390 0.000 2 -309.089 624.178 638.356 102.471 832
Total.Bsmt.SF.log 0.156 0.155 0.351 154.036 0.000 2 -309.238 624.476 638.655 102.507 832
Bsmt.Exposure 0.142 0.141 0.354 137.608 0.000 2 -316.244 638.488 652.667 104.244 832
Bsmt.Full.Bath 0.106 0.105 0.361 99.048 0.000 2 -333.167 672.333 686.512 108.562 832
Half.Bath 0.104 0.103 0.362 96.471 0.000 2 -334.323 674.645 688.824 108.863 832
Lot.Shape 0.089 0.088 0.365 81.355 0.000 2 -341.167 688.334 702.513 110.664 832
Garage.Finish 0.082 0.081 0.366 74.016 0.000 2 -344.531 695.063 709.241 111.561 832
Bedroom.AbvGr 0.074 0.073 0.368 66.509 0.000 2 -348.001 702.002 716.180 112.493 832
Lot.Area 0.064 0.063 0.370 56.772 0.000 2 -352.545 711.089 725.268 113.725 832
Enclosed.Porch.log 0.058 0.057 0.371 51.191 0.000 2 -355.172 716.344 730.522 114.444 832
Bsmt.Unf.SF.sqrt 0.038 0.037 0.375 33.255 0.000 2 -363.727 733.455 747.633 116.816 832
X2nd.Flr.SF.log 0.031 0.030 0.376 26.838 0.000 2 -366.831 739.662 753.841 117.689 832
Screen.Porch.log 0.009 0.008 0.380 7.672 0.006 2 -376.243 758.485 772.664 120.376 832
Low.Qual.Fin.SF.log 0.008 0.007 0.381 6.813 0.009 2 -376.669 759.339 773.517 120.499 832
Overall.Cond 0.006 0.005 0.381 4.801 0.029 2 -377.671 761.342 775.520 120.789 832
Mo.Sold 0.004 0.002 0.381 2.933 0.087 2 -378.603 763.206 777.384 121.059 832
BsmtFin.SF.2.log 0.000 -0.001 0.382 0.167 0.683 2 -379.986 765.973 780.151 121.461 832
Yr.Sold 0.000 -0.001 0.382 0.117 0.732 2 -380.011 766.023 780.201 121.468 832
X3Ssn.Porch 0.000 -0.001 0.382 0.015 0.902 2 -380.063 766.125 780.304 121.483 832
X3Ssn.Porch.log 0.000 -0.001 0.382 0.000 0.996 2 -380.070 766.140 780.319 121.486 832

Predictor Regression Analysis

Predictor Correlation Analysis

Label.1 Variable.1 Label.2 Variable.2 r
f22 age.log f23 age.garage.log 0.9245
f19 X3Ssn.Porch f39 X3Ssn.Porch.log 0.9233
f15 Fireplaces f16 Fireplace.Qu 0.8558
f25 area.log f35 TotRms.AbvGrd.log 0.7932
f3 Overall.Qual f5 Exter.Qual 0.7048
f6 Bsmt.Qual f34 Total.Bsmt.SF.log 0.7017
f5 Exter.Qual f14 Kitchen.Qual 0.7009
f13 Bedroom.AbvGr f35 TotRms.AbvGrd.log 0.7008
f18 Garage.Cars f28 Garage.Area.log 0.6891
f1 Lot.Area f29 Lot.Area.log 0.6674
f11 Full.Bath f25 area.log 0.6653
f22 age.log f24 age.remod.log 0.6622
f23 age.garage.log f24 age.remod.log 0.6435
f3 Overall.Qual f14 Kitchen.Qual 0.6433
f3 Overall.Qual f6 Bsmt.Qual 0.6067
f3 Overall.Qual f25 area.log 0.5931
f12 Half.Bath f38 X2nd.Flr.SF.log 0.5839
f13 Bedroom.AbvGr f25 area.log 0.5838
f3 Overall.Qual f18 Garage.Cars 0.5790
f8 BsmtFin.Type.1 f10 Bsmt.Full.Bath 0.5584
f25 area.log f38 X2nd.Flr.SF.log 0.5547
f11 Full.Bath f35 TotRms.AbvGrd.log 0.5412
f3 Overall.Qual f11 Full.Bath 0.5348
f25 area.log f37 X1st.Flr.SF.log 0.5288
f16 Fireplace.Qu f25 area.log 0.5285
f18 Garage.Cars f25 area.log 0.5190
f5 Exter.Qual f6 Bsmt.Qual 0.5133
f15 Fireplaces f25 area.log 0.5024

2018-08-07